1. Frequency polygons in which the number of observations at each temperature is reduced to a percentage basis while the time factor is represented on a logarithmic scale, indicate that the time required by Paramecium to swim a unit distance at different temperatures varies within definite limits which are constant above 15°. Below 15° the range of variability very possibly is not the same, though probably likewise constant.
2. Logarithmic velocities deduced from mean, maximal, minimal, and modal time classes, when plotted against reciprocals of the absolute temperature, fall respectively on straight lines. These lines are parallel and give µ values of 8,000 above 15° and probably 16,000 below.
3. This implies that the mechanism of locomotion in Paramecium remains essentially unaltered by a rise in temperature from 15° to 30°, and probably remains in a similar sense constant from 6° to 15°.
4. The theoretical interpretation of this result is possible in terms of a catenary series 0 → A → E in which the passages 0 → A and A → E are controlled by two catalysts differing respectively in concentration in different individuals and perhaps at different times in the same individual, but depending for their effective concentration on reactions having temperature coefficients identical with those which at each temperature characterize the biological process under consideration.
On the Berry-Esséen bound of frequency polygons for ϕ-mixing samples
